[daip] XMOM question

[Eric Greisen]

On 10/03/2017 10:35 AM, Lawrence Rudnick wrote:
> Hi Eric -  curious question. given past history, likely user error, but 
> i can't find it.
> 
> Running XMOM on a (nonstandard) map with Faraday spectra along rows 
> (blanked at amplitude of 1e-5). Can't understand moments 0 and 2.
> 
>    Here is the header and the moments calculated on row 483 of the 
> following image:
> 
> AIPS 1: Image=A2256     (MA) Filename=A2256SA16C_R.FAMPRO.   1
> AIPS 1: Magic value blanking
> AIPS 1: Minimum=  10.0002            Maximum=  48.5521 MicroJY/BEAM
> AIPS 1: --------------------------------------------------------------
> AIPS 1: Type    Pixels   Coord value  at Pixel    Coord incr Rotat
> AIPS 1: ANGLE-PAIR AXES INCONSISTENT OR PARTLY MISSING
> AIPS 1: RAD/M2     801    0.000000E+00     401*   5.0000E+00 0.00
> AIPS 1: RA---SIN   600    17 03 37.300     300*    -0.150000 0.00
> AIPS 1: --------------------------------------------------------------
> AIPS 1: Map type=NORMAL              Number of iterations=   32332
> AIPS 1: Conv size=   1.40 X   1.40   Position angle=   0.00
> AIPS 1: Max ext file #: HI   1    SL   3
> AIPS 1: * => NOT the formal reference pixel on this axis
> AIPS 1: '483_88_0.008211_-155.8096_113.8049'
> 
> XMOMNC  88
> XMOM0 0.0082  guess about 23 microJy
> XMOM1 -155  looks about right
> XMOM2 113.8 about HWHM^2=125^2, so looks like sqrt(2nd moment)?
> 

Yes moment 0 is the sum of the "brightnesses".  Moment 1 is
sum(f(i) * i) / sum (f(i)).  Moment 2 is the usual rms sort of 
computation:  SQRT ( sum(f(i)*i*i)/sum(f(i)) - Mom1*Mom1)

I think this is the second moment rather than the sqrt (2nd moment)

Eric